Cos^2x-10sinx+10=0
Cos^2x = 1 - Sin^2x
1 - Sin^2x - 10Sinx + 10 = 0
-Sin^2x - 10Sinx + 11 = 0
t = Sinx ∈ [-1;1]
-t^2 - 10t + 11 = 0
D = 100 - 4 * (-1) * 11 = 144
t1 = (10 + √144) / -2 = -11 ∉ [-1;1]
t2 = (10 - √144) / -2 = 1
Sinx = 1 => x = π/2 + 2πn, n ∈ Z